Question

A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of 200 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $300. Inventory holding costs will be $10 a year.

a. What run quantity should be used to minimize total annual costs?

b. How many days does it take to produce the optimal run quantity?

c. What is the average amount of inventory?

Answer 1

a. What run quantity should be used to minimize total annual costs?

We have following information:

Daily demand = 80 units

Demand for 1 week = 80 * 5 = 400 units

Annual demand, D = 400 *50 = 20,000 units

Set-up cost S = $300 per order

Annual Inventory holding cost, H = $10 per unit per year

Economic order quantity is the run quantity to minimize the total annual cost

Formula of economic production quantity (EPQ)

EPQ = Q = √ (2 * Annual Demand * Set-up cost/ Inventory holding cost)

Therefore

EPQ = Q = √ (2 * 20,000 *$300 / $10)

EPQ = Q =√ (1,200,000) = 1,095.45 or 1,095 units (rounding off to nearest whole number)

The run quantity to minimize the total annual cost is 1,095 units

b. How many days does it take to produce the optimal run quantity?

The machine will produce the item at a rate of 200 units a day

Therefore,

Length of production run for the optimal run quantity = economic production quantity/ production per day

= 1,095 units /200

= 5.48 days

It will take 5.48 days to produce the optimal run quantity

c. What is the average amount of inventory?

Average inventory level = EPQ / 2 = 1,095 /2 = 547.5 or 548 units